0.25t^2+7t+45=0

Solution for 0.25t^2+7t+45=0 equation:

Simplifying
0.25t2 + 7t + 45 = 0

Reorder the terms:
45 + 7t + 0.25t2 = 0

Solving
45 + 7t + 0.25t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
0.25 the coefficient of the squared term: 

Divide each side by '0.25'.
180 + 28t + t2 = 0

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + 28t + -180 + t2 = 0 + -180

Reorder the terms:
180 + -180 + 28t + t2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + 28t + t2 = 0 + -180
28t + t2 = 0 + -180

Combine like terms: 0 + -180 = -180
28t + t2 = -180

The t term is 28t.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28t + 196 + t2 = -180 + 196

Reorder the terms:
196 + 28t + t2 = -180 + 196

Combine like terms: -180 + 196 = 16
196 + 28t + t2 = 16

Factor a perfect square on the left side:
(t + 14)(t + 14) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(t + 14) equal to 4 and -4.

Subproblem 1
t + 14 = 4

Simplifying
t + 14 = 4

Reorder the terms:
14 + t = 4

Solving
14 + t = 4

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -14 + t = 4 + -14

Combine like terms: 14 + -14 = 0
0 + t = 4 + -14
t = 4 + -14

Combine like terms: 4 + -14 = -10
t = -10

Simplifying
t = -10

Subproblem 2
t + 14 = -4

Simplifying
t + 14 = -4

Reorder the terms:
14 + t = -4

Solving
14 + t = -4

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -14 + t = -4 + -14

Combine like terms: 14 + -14 = 0
0 + t = -4 + -14
t = -4 + -14

Combine like terms: -4 + -14 = -18
t = -18

Simplifying
t = -18

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-10, -18}